| 时变参数下非线性扭振系统的Hopf分岔研究 |
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| 引用本文： | 刘彬,李延树,周磊,李海滨,刘爽.时变参数下非线性扭振系统的Hopf分岔研究[J].燕山大学学报,2011,35(6):533-537. |
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| 作者姓名： | 刘彬 李延树 周磊 李海滨 刘爽 |
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| 作者单位： | 1. 燕山大学电气工程学院,河北秦皇岛,066004
2. 大连市产品质量监督检验所,辽宁大连,116021 |
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| 基金项目： | 国家自然科学基金资助项目，河北省自然科学基金资助项目 |
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| 摘 要： | 建立了一类含时变刚度和非线性阻尼的两自由度非线性扭振系统动力学方程,利用多尺度方法推导出了系统的平均方程。根据Hopf分岔理论分析了系统稳定性,给出了系统发生Hopf分岔的充要条件及系统周期运动稳定性的判别方法,分析了主共振情况下超临界Hopf分岔和亚临界Hopf分岔对系统振荡的影响。最后通过数值仿真验证了结论的正确性,对确保该类扭振系统的稳定运行有一定指导意义。
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| 关 键 词： | 扭振系统 Hopf分岔 稳定性 |
Study on Hopf bifurcation due to time-varying parameter in nonlinear torsional vibration system |
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| LIU Bin,LI Yan-shu,ZHOU Lei,LI Hai-bin,LIU Shuang.Study on Hopf bifurcation due to time-varying parameter in nonlinear torsional vibration system[J].Journal of Yanshan University,2011,35(6):533-537. |
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| Authors: | LIU Bin LI Yan-shu ZHOU Lei LI Hai-bin LIU Shuang |
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| Institution: | 1(1.College of Electrical Engineering,Yanshan University,Qinhuangdao,Hebei 066004,China;2.Dalian Institute of Product Quality Supervision and Inspection,Dalian,Liaoning 116021,China) |
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| Abstract: | The nonlinear dynamic equation of torsional vibration system with two degrees of freedom is established including the time-varying stiffness and nonlinear damping.The average equation of system is deduced with the aid of multi-scale time method.Besides,according to Hopf bifurcation theory,the stability of system is analyzed,the necessary and sufficient condition of Hopf bifurcation and the judgment method of periodic motion’s stability are given,and the influence of supercritical and subcritical Hopf bifurcation on vibration of system is analyzed under the condition of primary resonance.Last,the numerical simulation verifies the results.A significant contribution of this study is to ensure smooth running of this kind of torsional vibration system. |
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| Keywords: | torsional vibration system Hopf bifurcation stability |
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